Problem: The geometric sequence $(a_i)$ is defined by the formula: $a_i = 5 \left(-2\right)^{i - 1}$ What is $a_{3}$, the third term in the sequence?
Answer: From the given formula, we can see that the first term of the sequence is $5$ and the common ratio is $-2$ To find $a_{3}$ , we can simply substitute $i = 3$ into the given formula. Therefore, the third term is equal to $a_{3} = 5 \left(-2\right)^{3 - 1} = 20$.